Risk-Neutral Pricing Model of Uniswap Liquidity Providing Position: A Stopping Time Approach

Paper: arXiv 2411.12375

Authors: Liang Hou, Hao Yu, Guosong Xu

Abstract

In this paper, we introduce a novel pricing model for Uniswap V3, built upon stochastic processes and the Martingale Stopping Theorem. This model innovatively frames the valuation of positions within Uniswap V3. We further conduct a numerical analysis and examine the sensitivities through Greek risk measures to elucidate the model’s implications. The results underscore the model’s significant academic contribution and its practical applicability for Uniswap liquidity providers, particularly in assessing risk exposure and guiding hedging strategies.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical derivation for pricing Uniswap V3 positions as perpetual derivatives using stochastic processes and the Martingale Stopping Theorem. However, the empirical validation is limited to basic Monte Carlo simulations rather than extensive backtesting on historical DEX market data.

Research Flowchart

  flowchart TD
    A[Research Goal: Risk-Neutral Pricing & Risk<br>Assessment for Uniswap V3 LP Positions] --> B[Data Inputs: Crypto Prices, Volatility,<br>Uniswap V3 Pool Parameters]
    B --> C[Methodology: Stochastic Processes &<br>Martingale Stopping Theorem]
    C --> D[Model Execution: Closed-Form Pricing &<br>Greek Sensitivity Calculation]
    D --> E[Key Outcomes: Optimal Hedging Strategies &<br>Quantified Impermanent Loss Risk]